In this paper we study an inverse problem governed by a constrained nonlinear elliptic quasi-variational hemivariational inequality. The inequality involves two nondifferentiable functions which directly depend on solutions. We solve the direct problem and obtain the properties of weak closedness and uniform boundedness of solutions, which develops some existing results in literature. Then, using a regularized optimization method, we deal with an inverse problem to seek the identification of parameter functions appearing in the leading operator and constraint set. Finally, we apply the abstract result to a concrete inverse problem of identifying the parameter and obstacle functions in elliptic obstacle problems with the $p$-Laplace operator and mixed boundary conditions.

在本文中，我们研究了一个受约束的非线性椭圆准变半变分不等式控制的逆问题。不等式包含两个直接取决于解的不可微函数。我们解决了直接问题，并获得了弱闭合性和解的有界界的性质，这在文献中得到了一些已有的结果。然后，使用正则化优化方法，处理一个反问题，以寻找出现在前导算子和约束集中的参数函数的标识。最后，我们将抽象结果应用到一个具体的反问题中，该椭圆问题用于识别椭圆障碍问题中的参数和障碍函数。$p$-拉普拉斯算子和混合边界条件。